LMFDB - Embedded newform 285.2.c.b.229.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,2,Mod(229,285)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("285.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 285 = 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	285.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.27573645761$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 25x^{12} + 242x^{10} + 1134x^{8} + 2605x^{6} + 2545x^{4} + 552x^{2} + 16 $ x^14 + 25x^12 + 242x^10 + 1134x^8 + 2605x^6 + 2545x^4 + 552x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			229.13
Root			$2.47637i$ of defining polynomial
Character	$\chi$	$=$	285.229
Dual form			285.2.c.b.229.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.47637i q^{2} -1.00000i q^{3} -4.13242 q^{4} +(-0.164064 - 2.23004i) q^{5} +2.47637 q^{6} -3.36493i q^{7} -5.28066i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+2.47637i q^{2} -1.00000i q^{3} -4.13242 q^{4} +(-0.164064 - 2.23004i) q^{5} +2.47637 q^{6} -3.36493i q^{7} -5.28066i q^{8} -1.00000 q^{9} +(5.52241 - 0.406282i) q^{10} +3.04014 q^{11} +4.13242i q^{12} -3.21982i q^{13} +8.33281 q^{14} +(-2.23004 + 0.164064i) q^{15} +4.81205 q^{16} +3.46548i q^{17} -2.47637i q^{18} -1.00000 q^{19} +(0.677979 + 9.21547i) q^{20} -3.36493 q^{21} +7.52852i q^{22} -7.11300i q^{23} -5.28066 q^{24} +(-4.94617 + 0.731737i) q^{25} +7.97346 q^{26} +1.00000i q^{27} +13.9053i q^{28} +8.97685 q^{29} +(-0.406282 - 5.52241i) q^{30} -3.11926 q^{31} +1.35510i q^{32} -3.04014i q^{33} -8.58181 q^{34} +(-7.50392 + 0.552062i) q^{35} +4.13242 q^{36} +0.438901i q^{37} -2.47637i q^{38} -3.21982 q^{39} +(-11.7761 + 0.866365i) q^{40} -2.71201 q^{41} -8.33281i q^{42} +7.50511i q^{43} -12.5631 q^{44} +(0.164064 + 2.23004i) q^{45} +17.6144 q^{46} +6.31163i q^{47} -4.81205i q^{48} -4.32273 q^{49} +(-1.81205 - 12.2485i) q^{50} +3.46548 q^{51} +13.3056i q^{52} -2.14845i q^{53} -2.47637 q^{54} +(-0.498776 - 6.77964i) q^{55} -17.7690 q^{56} +1.00000i q^{57} +22.2300i q^{58} +11.0711 q^{59} +(9.21547 - 0.677979i) q^{60} -7.09357 q^{61} -7.72446i q^{62} +3.36493i q^{63} +6.26836 q^{64} +(-7.18032 + 0.528254i) q^{65} +7.52852 q^{66} -13.3097i q^{67} -14.3208i q^{68} -7.11300 q^{69} +(-1.36711 - 18.5825i) q^{70} +13.3097 q^{71} +5.28066i q^{72} +1.62020i q^{73} -1.08688 q^{74} +(0.731737 + 4.94617i) q^{75} +4.13242 q^{76} -10.2298i q^{77} -7.97346i q^{78} +8.09580 q^{79} +(-0.789482 - 10.7311i) q^{80} +1.00000 q^{81} -6.71595i q^{82} +15.4581i q^{83} +13.9053 q^{84} +(7.72816 - 0.568559i) q^{85} -18.5854 q^{86} -8.97685i q^{87} -16.0540i q^{88} -5.69208 q^{89} +(-5.52241 + 0.406282i) q^{90} -10.8344 q^{91} +29.3939i q^{92} +3.11926i q^{93} -15.6299 q^{94} +(0.164064 + 2.23004i) q^{95} +1.35510 q^{96} +8.82840i q^{97} -10.7047i q^{98} -3.04014 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 22 q^{4} + 2 q^{5} + 6 q^{6} - 14 q^{9}+O(q^{10}) $ 14 * q - 22 * q^4 + 2 * q^5 + 6 * q^6 - 14 * q^9	$ 14 q - 22 q^{4} + 2 q^{5} + 6 q^{6} - 14 q^{9} + 2 q^{10} - 8 q^{11} + 8 q^{14} - 2 q^{15} + 38 q^{16} - 14 q^{19} + 12 q^{20} + 16 q^{21} - 18 q^{24} - 4 q^{25} - 40 q^{26} + 12 q^{29} + 4 q^{30} + 8 q^{31} - 4 q^{34} - 14 q^{35} + 22 q^{36} - 16 q^{39} + 18 q^{40} + 4 q^{41} + 64 q^{44} - 2 q^{45} - 8 q^{46} - 34 q^{49} + 4 q^{50} + 8 q^{51} - 6 q^{54} - 2 q^{55} - 44 q^{56} + 36 q^{59} - 18 q^{60} + 24 q^{61} - 22 q^{64} - 12 q^{65} + 24 q^{66} - 20 q^{69} - 60 q^{70} - 36 q^{71} - 12 q^{74} + 22 q^{76} + 8 q^{79} + 36 q^{80} + 14 q^{81} - 28 q^{84} - 18 q^{85} - 92 q^{86} + 16 q^{89} - 2 q^{90} + 24 q^{91} + 40 q^{94} - 2 q^{95} + 62 q^{96} + 8 q^{99}+O(q^{100}) $ 14 * q - 22 * q^4 + 2 * q^5 + 6 * q^6 - 14 * q^9 + 2 * q^10 - 8 * q^11 + 8 * q^14 - 2 * q^15 + 38 * q^16 - 14 * q^19 + 12 * q^20 + 16 * q^21 - 18 * q^24 - 4 * q^25 - 40 * q^26 + 12 * q^29 + 4 * q^30 + 8 * q^31 - 4 * q^34 - 14 * q^35 + 22 * q^36 - 16 * q^39 + 18 * q^40 + 4 * q^41 + 64 * q^44 - 2 * q^45 - 8 * q^46 - 34 * q^49 + 4 * q^50 + 8 * q^51 - 6 * q^54 - 2 * q^55 - 44 * q^56 + 36 * q^59 - 18 * q^60 + 24 * q^61 - 22 * q^64 - 12 * q^65 + 24 * q^66 - 20 * q^69 - 60 * q^70 - 36 * q^71 - 12 * q^74 + 22 * q^76 + 8 * q^79 + 36 * q^80 + 14 * q^81 - 28 * q^84 - 18 * q^85 - 92 * q^86 + 16 * q^89 - 2 * q^90 + 24 * q^91 + 40 * q^94 - 2 * q^95 + 62 * q^96 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/285\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$211$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			2.47637i			1.75106i	0.483164	+	0.875530i	$0.339487\pi$
$2$			2.47637i			1.75106i	−0.483164	+	0.875530i	$0.660513\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−4.13242			−2.06621
$5$	−0.164064	−	2.23004i	−0.0733714	−	0.997305i
$5$	−0.164064	−	2.23004i	−0.0733714	−	0.997305i
$6$	2.47637			1.01097
$7$		−	3.36493i		−	1.27182i	−0.771762	−	0.635911i	$-0.780624\pi$
$7$		−	3.36493i		−	1.27182i	0.771762	−	0.635911i	$-0.219376\pi$
$8$		−	5.28066i		−	1.86700i
$9$	−1.00000			−0.333333
$10$	5.52241	−	0.406282i	1.74634	−	0.128478i
$11$	3.04014			0.916637			0.458318	−	0.888788i	$-0.348452\pi$
$11$	3.04014			0.916637			0.458318	+	0.888788i	$0.348452\pi$
$12$			4.13242i			1.19293i
$13$		−	3.21982i		−	0.893016i	−0.894780	−	0.446508i	$-0.852667\pi$
$13$		−	3.21982i		−	0.893016i	0.894780	−	0.446508i	$-0.147333\pi$
$14$	8.33281			2.22704
$15$	−2.23004	+	0.164064i	−0.575794	+	0.0423610i
$16$	4.81205			1.20301
$17$			3.46548i			0.840502i	0.907408	+	0.420251i	$0.138058\pi$
$17$			3.46548i			0.840502i	−0.907408	+	0.420251i	$0.861942\pi$
$18$		−	2.47637i		−	0.583687i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	0.677979	+	9.21547i	0.151601	+	2.06064i
$21$	−3.36493			−0.734287
$22$			7.52852i			1.60509i
$23$		−	7.11300i		−	1.48316i	−0.670863	−	0.741581i	$-0.734076\pi$
$23$		−	7.11300i		−	1.48316i	0.670863	−	0.741581i	$-0.265924\pi$
$24$	−5.28066			−1.07791
$25$	−4.94617	+	0.731737i	−0.989233	+	0.146347i
$26$	7.97346			1.56372
$27$			1.00000i			0.192450i
$28$			13.9053i			2.62785i
$29$	8.97685			1.66696			0.833480	−	0.552550i	$-0.186345\pi$
$29$	8.97685			1.66696			0.833480	+	0.552550i	$0.186345\pi$
$30$	−0.406282	−	5.52241i	−0.0741767	−	1.00825i
$31$	−3.11926			−0.560236			−0.280118	−	0.959966i	$-0.590374\pi$
$31$	−3.11926			−0.560236			−0.280118	+	0.959966i	$0.590374\pi$
$32$			1.35510i			0.239551i
$33$		−	3.04014i		−	0.529220i
$34$	−8.58181			−1.47177
$35$	−7.50392	+	0.552062i	−1.26839	+	0.0933155i
$36$	4.13242			0.688737
$37$			0.438901i			0.0721550i	0.999349	+	0.0360775i	$0.0114863\pi$
$37$			0.438901i			0.0721550i	−0.999349	+	0.0360775i	$0.988514\pi$
$38$		−	2.47637i		−	0.401721i
$39$	−3.21982			−0.515583
$40$	−11.7761	+	0.866365i	−1.86196	+	0.136984i
$41$	−2.71201			−0.423545			−0.211773	−	0.977319i	$-0.567924\pi$
$41$	−2.71201			−0.423545			−0.211773	+	0.977319i	$0.567924\pi$
$42$		−	8.33281i		−	1.28578i
$43$			7.50511i			1.14452i	0.820073	+	0.572259i	$0.193933\pi$
$43$			7.50511i			1.14452i	−0.820073	+	0.572259i	$0.806067\pi$
$44$	−12.5631			−1.89396
$45$	0.164064	+	2.23004i	0.0244571	+	0.332435i
$46$	17.6144			2.59711
$47$			6.31163i			0.920646i	0.887752	+	0.460323i	$0.152266\pi$
$47$			6.31163i			0.920646i	−0.887752	+	0.460323i	$0.847734\pi$
$48$		−	4.81205i		−	0.694560i
$49$	−4.32273			−0.617533
$50$	−1.81205	−	12.2485i	−0.256263	−	1.73221i
$51$	3.46548			0.485264
$52$			13.3056i			1.84516i
$53$		−	2.14845i		−	0.295113i	−0.989054	−	0.147556i	$-0.952859\pi$
$53$		−	2.14845i		−	0.295113i	0.989054	−	0.147556i	$-0.0471408\pi$
$54$	−2.47637			−0.336992
$55$	−0.498776	−	6.77964i	−0.0672550	−	0.914166i
$56$	−17.7690			−2.37449
$57$			1.00000i			0.132453i
$58$			22.2300i			2.91895i
$59$	11.0711			1.44134			0.720670	−	0.693279i	$-0.243834\pi$
$59$	11.0711			1.44134			0.720670	+	0.693279i	$0.243834\pi$
$60$	9.21547	−	0.677979i	1.18971	−	0.0875268i
$61$	−7.09357			−0.908239			−0.454119	−	0.890941i	$-0.650046\pi$
$61$	−7.09357			−0.908239			−0.454119	+	0.890941i	$0.650046\pi$
$62$		−	7.72446i		−	0.981007i
$63$			3.36493i			0.423941i
$64$	6.26836			0.783545
$65$	−7.18032	+	0.528254i	−0.890609	+	0.0655219i
$66$	7.52852			0.926697
$67$		−	13.3097i		−	1.62603i	−0.582240	−	0.813017i	$-0.697824\pi$
$67$		−	13.3097i		−	1.62603i	0.582240	−	0.813017i	$-0.302176\pi$
$68$		−	14.3208i		−	1.73665i
$69$	−7.11300			−0.856304
$70$	−1.36711	−	18.5825i	−0.163401	−	2.22103i
$71$	13.3097			1.57957			0.789783	−	0.613386i	$-0.210193\pi$
$71$	13.3097			1.57957			0.789783	+	0.613386i	$0.210193\pi$
$72$			5.28066i			0.622332i
$73$			1.62020i			0.189630i	0.995495	+	0.0948149i	$0.0302259\pi$
$73$			1.62020i			0.189630i	−0.995495	+	0.0948149i	$0.969774\pi$
$74$	−1.08688			−0.126348
$75$	0.731737	+	4.94617i	0.0844937	+	0.571134i
$76$	4.13242			0.474021
$77$		−	10.2298i		−	1.16580i
$78$		−	7.97346i		−	0.902817i
$79$	8.09580			0.910849			0.455424	−	0.890274i	$-0.349488\pi$
$79$	8.09580			0.910849			0.455424	+	0.890274i	$0.349488\pi$
$80$	−0.789482	−	10.7311i	−0.0882668	−	1.19977i
$81$	1.00000			0.111111
$82$		−	6.71595i		−	0.741653i
$83$			15.4581i			1.69675i	0.529397	+	0.848374i	$0.322418\pi$
$83$			15.4581i			1.69675i	−0.529397	+	0.848374i	$0.677582\pi$
$84$	13.9053			1.51719
$85$	7.72816	−	0.568559i	0.838237	−	0.0616688i
$86$	−18.5854			−2.00412
$87$		−	8.97685i		−	0.962420i
$88$		−	16.0540i		−	1.71136i
$89$	−5.69208			−0.603359			−0.301679	−	0.953409i	$-0.597547\pi$
$89$	−5.69208			−0.603359			−0.301679	+	0.953409i	$0.597547\pi$
$90$	−5.52241	+	0.406282i	−0.582113	+	0.0428259i
$91$	−10.8344			−1.13576
$92$			29.3939i			3.06452i
$93$			3.11926i			0.323453i
$94$	−15.6299			−1.61211
$95$	0.164064	+	2.23004i	0.0168326	+	0.228797i
$96$	1.35510			0.138305
$97$			8.82840i			0.896388i	0.893936	+	0.448194i	$0.147933\pi$
$97$			8.82840i			0.896388i	−0.893936	+	0.448194i	$0.852067\pi$
$98$		−	10.7047i		−	1.08134i
$99$	−3.04014			−0.305546
$100$	20.4396	−	3.02384i	2.04396	−	0.302384i
$101$	−17.7011			−1.76132			−0.880662	−	0.473746i	$-0.842901\pi$
$101$	−17.7011			−1.76132			−0.880662	+	0.473746i	$0.842901\pi$
$102$			8.58181i			0.849726i
$103$		−	18.5287i		−	1.82569i	−0.408304	−	0.912846i	$-0.633880\pi$
$103$		−	18.5287i		−	1.82569i	0.408304	−	0.912846i	$-0.366120\pi$
$104$	−17.0028			−1.66726
$105$	0.552062	+	7.50392i	0.0538757	+	0.732308i
$106$	5.32037			0.516760
$107$			10.7299i			1.03729i	0.854988	+	0.518647i	$0.173564\pi$
$107$			10.7299i			1.03729i	−0.854988	+	0.518647i	$0.826436\pi$
$108$		−	4.13242i		−	0.397642i
$109$	4.26484			0.408498			0.204249	−	0.978919i	$-0.434525\pi$
$109$	4.26484			0.408498			0.204249	+	0.978919i	$0.434525\pi$
$110$	16.7889	−	1.23516i	1.60076	−	0.117767i
$111$	0.438901			0.0416587
$112$		−	16.1922i		−	1.53002i
$113$			13.5016i			1.27012i	0.772463	+	0.635060i	$0.219025\pi$
$113$			13.5016i			1.27012i	−0.772463	+	0.635060i	$0.780975\pi$
$114$	−2.47637			−0.231934
$115$	−15.8623	+	1.16698i	−1.47916	+	0.108822i
$116$	−37.0961			−3.44429
$117$			3.21982i			0.297672i
$118$			27.4163i			2.52387i
$119$	11.6611			1.06897
$120$	0.866365	+	11.7761i	0.0790879	+	1.07501i
$121$	−1.75755			−0.159777
$122$		−	17.5663i		−	1.59038i
$123$			2.71201i			0.244534i
$124$	12.8901			1.15757
$125$	2.44329	+	10.9101i	0.218534	+	0.975829i
$126$	−8.33281			−0.742346
$127$			6.15097i			0.545811i	0.962041	+	0.272905i	$0.0879846\pi$
$127$			6.15097i			0.545811i	−0.962041	+	0.272905i	$0.912015\pi$
$128$			18.2330i			1.61159i
$129$	7.50511			0.660788
$130$	−1.30815	−	17.7811i	−0.114733	−	1.55951i
$131$	9.61327			0.839915			0.419958	−	0.907544i	$-0.362045\pi$
$131$	9.61327			0.839915			0.419958	+	0.907544i	$0.362045\pi$
$132$			12.5631i			1.09348i
$133$			3.36493i			0.291776i
$134$	32.9597			2.84728
$135$	2.23004	−	0.164064i	0.191931	−	0.0141203i
$136$	18.3000			1.56921
$137$		−	11.8850i		−	1.01541i	−0.861532	−	0.507704i	$-0.830495\pi$
$137$		−	11.8850i		−	1.01541i	0.861532	−	0.507704i	$-0.169505\pi$
$138$		−	17.6144i		−	1.49944i
$139$	6.94000			0.588643			0.294322	−	0.955706i	$-0.404906\pi$
$139$	6.94000			0.588643			0.294322	+	0.955706i	$0.404906\pi$
$140$	31.0094	−	2.28135i	2.62077	−	0.192809i
$141$	6.31163			0.531535
$142$			32.9597i			2.76591i
$143$		−	9.78869i		−	0.818571i
$144$	−4.81205			−0.401004
$145$	−1.47277	−	20.0187i	−0.122307	−	1.66247i
$146$	−4.01221			−0.332053
$147$			4.32273i			0.356533i
$148$		−	1.81373i		−	0.149087i
$149$	0.387098			0.0317123			0.0158561	−	0.999874i	$-0.494953\pi$
$149$	0.387098			0.0317123			0.0158561	+	0.999874i	$0.494953\pi$
$150$	−12.2485	+	1.81205i	−1.00009	+	0.147953i
$151$	15.8112			1.28670			0.643349	−	0.765573i	$-0.277545\pi$
$151$	15.8112			1.28670			0.643349	+	0.765573i	$0.277545\pi$
$152$			5.28066i			0.428318i
$153$		−	3.46548i		−	0.280167i
$154$	25.3329			2.04138
$155$	0.511757	+	6.95608i	0.0411053	+	0.558726i
$156$	13.3056			1.06530
$157$			15.7969i			1.26073i	0.776300	+	0.630364i	$0.217094\pi$
$157$			15.7969i			1.26073i	−0.776300	+	0.630364i	$0.782906\pi$
$158$			20.0482i			1.59495i
$159$	−2.14845			−0.170383
$160$	3.02194	−	0.222323i	0.238905	−	0.0175762i
$161$	−23.9347			−1.88632
$162$			2.47637i			0.194562i
$163$		−	6.38877i		−	0.500407i	−0.968193	−	0.250204i	$-0.919502\pi$
$163$		−	6.38877i		−	0.500407i	0.968193	−	0.250204i	$-0.0804975\pi$
$164$	11.2072			0.875133
$165$	−6.77964	+	0.498776i	−0.527794	+	0.0388297i
$166$	−38.2800			−2.97111
$167$			20.4619i			1.58339i	0.610916	+	0.791695i	$0.290801\pi$
$167$			20.4619i			1.58339i	−0.610916	+	0.791695i	$0.709199\pi$
$168$			17.7690i			1.37091i
$169$	2.63279			0.202522
$170$	1.40796	+	19.1378i	0.107986	+	1.46780i
$171$	1.00000			0.0764719
$172$		−	31.0142i		−	2.36481i
$173$		−	11.2123i		−	0.852453i	−0.904616	−	0.426227i	$-0.859843\pi$
$173$		−	11.2123i		−	0.852453i	0.904616	−	0.426227i	$-0.140157\pi$
$174$	22.2300			1.68525
$175$	2.46224	+	16.6435i	0.186128	+	1.25813i
$176$	14.6293			1.10273
$177$		−	11.0711i		−	0.832158i
$178$		−	14.0957i		−	1.05652i
$179$	0.236476			0.0176750			0.00883752	−	0.999961i	$-0.497187\pi$
$179$	0.236476			0.0176750			0.00883752	+	0.999961i	$0.497187\pi$
$180$	−0.677979	−	9.21547i	−0.0505336	−	0.686880i
$181$	−6.52968			−0.485347			−0.242674	−	0.970108i	$-0.578024\pi$
$181$	−6.52968			−0.485347			−0.242674	+	0.970108i	$0.578024\pi$
$182$		−	26.8301i		−	1.98878i
$183$			7.09357i			0.524372i
$184$	−37.5613			−2.76906
$185$	0.978768	−	0.0720077i	0.0719605	−	0.00529411i
$186$	−7.72446			−0.566385
$187$			10.5355i			0.770435i
$188$		−	26.0823i		−	1.90225i
$189$	3.36493			0.244762
$190$	−5.52241	+	0.406282i	−0.400638	+	0.0294748i
$191$	8.12841			0.588151			0.294076	−	0.955782i	$-0.404988\pi$
$191$	8.12841			0.588151			0.294076	+	0.955782i	$0.404988\pi$
$192$		−	6.26836i		−	0.452380i
$193$			1.81373i			0.130555i	0.997867	+	0.0652774i	$0.0207932\pi$
$193$			1.81373i			0.130555i	−0.997867	+	0.0652774i	$0.979207\pi$
$194$	−21.8624			−1.56963
$195$	0.528254	+	7.18032i	0.0378291	+	0.514193i
$196$	17.8633			1.27595
$197$			7.19379i			0.512536i	0.966606	+	0.256268i	$0.0824930\pi$
$197$			7.19379i			0.512536i	−0.966606	+	0.256268i	$0.917507\pi$
$198$		−	7.52852i		−	0.535028i
$199$	0.290530			0.0205952			0.0102976	−	0.999947i	$-0.496722\pi$
$199$	0.290530			0.0205952			0.0102976	+	0.999947i	$0.496722\pi$
$200$	3.86406	+	26.1190i	0.273230	+	1.84690i
$201$	−13.3097			−0.938791
$202$		−	43.8345i		−	3.08418i
$203$		−	30.2064i		−	2.12008i
$204$	−14.3208			−1.00266
$205$	0.444942	+	6.04790i	0.0310761	+	0.422404i
$206$	45.8841			3.19690
$207$			7.11300i			0.494387i
$208$		−	15.4939i		−	1.07431i
$209$	−3.04014			−0.210291
$210$	−18.5825	+	1.36711i	−1.28232	+	0.0943396i
$211$	−7.46586			−0.513971			−0.256985	−	0.966415i	$-0.582729\pi$
$211$	−7.46586			−0.513971			−0.256985	+	0.966415i	$0.582729\pi$
$212$			8.87831i			0.609764i
$213$		−	13.3097i		−	0.911963i
$214$	−26.5711			−1.81636
$215$	16.7367	−	1.23131i	1.14143	−	0.0839749i
$216$	5.28066			0.359304
$217$			10.4961i			0.712521i
$218$			10.5613i			0.715304i
$219$	1.62020			0.109483
$220$	2.06115	+	28.0163i	0.138963	+	1.88886i
$221$	11.1582			0.750582
$222$			1.08688i			0.0729468i
$223$		−	27.8511i		−	1.86505i	−0.361107	−	0.932525i	$-0.617601\pi$
$223$		−	27.8511i		−	1.86505i	0.361107	−	0.932525i	$-0.382399\pi$
$224$	4.55983			0.304666
$225$	4.94617	−	0.731737i	0.329744	−	0.0487825i
$226$	−33.4349			−2.22406
$227$		−	17.4406i		−	1.15757i	−0.815480	−	0.578785i	$-0.803527\pi$
$227$		−	17.4406i		−	1.15757i	0.815480	−	0.578785i	$-0.196473\pi$
$228$		−	4.13242i		−	0.273676i
$229$	−6.97146			−0.460687			−0.230343	−	0.973109i	$-0.573985\pi$
$229$	−6.97146			−0.460687			−0.230343	+	0.973109i	$0.573985\pi$
$230$	−2.88988	−	39.2809i	−0.190553	−	2.59011i
$231$	−10.2298			−0.673075
$232$		−	47.4037i		−	3.11221i
$233$		−	8.73376i		−	0.572168i	−0.958205	−	0.286084i	$-0.907646\pi$
$233$		−	8.73376i		−	0.572168i	0.958205	−	0.286084i	$-0.0923536\pi$
$234$	−7.97346			−0.521241
$235$	14.0752	−	1.03551i	0.918164	−	0.0675491i
$236$	−45.7506			−2.97811
$237$		−	8.09580i		−	0.525879i
$238$			28.8772i			1.87183i
$239$	11.9784			0.774816			0.387408	−	0.921908i	$-0.373370\pi$
$239$	11.9784			0.774816			0.387408	+	0.921908i	$0.373370\pi$
$240$	−10.7311	+	0.789482i	−0.692688	+	0.0509609i
$241$	18.4362			1.18758			0.593790	−	0.804620i	$-0.297631\pi$
$241$	18.4362			1.18758			0.593790	+	0.804620i	$0.297631\pi$
$242$		−	4.35235i		−	0.279779i
$243$		−	1.00000i		−	0.0641500i
$244$	29.3136			1.87661
$245$	0.709202	+	9.63987i	0.0453093	+	0.615869i
$246$	−6.71595			−0.428194
$247$			3.21982i			0.204872i
$248$			16.4718i			1.04596i
$249$	15.4581			0.979618
$250$	−27.0175	+	6.05049i	−1.70874	+	0.382667i
$251$	14.3916			0.908392			0.454196	−	0.890902i	$-0.349927\pi$
$251$	14.3916			0.908392			0.454196	+	0.890902i	$0.349927\pi$
$252$		−	13.9053i		−	0.875951i
$253$		−	21.6245i		−	1.35952i
$254$	−15.2321			−0.955747
$255$	−0.568559	−	7.72816i	−0.0356045	−	0.483956i
$256$	−32.6150			−2.03844
$257$		−	13.4124i		−	0.836645i	−0.908298	−	0.418323i	$-0.862618\pi$
$257$		−	13.4124i		−	0.836645i	0.908298	−	0.418323i	$-0.137382\pi$
$258$			18.5854i			1.15708i
$259$	1.47687			0.0917683
$260$	29.6721	−	2.18297i	1.84019	−	0.135382i
$261$	−8.97685			−0.555653
$262$			23.8060i			1.47074i
$263$		−	3.84903i		−	0.237341i	−0.992934	−	0.118671i	$-0.962137\pi$
$263$		−	3.84903i		−	0.237341i	0.992934	−	0.118671i	$-0.0378633\pi$
$264$	−16.0540			−0.988053
$265$	−4.79114	+	0.352483i	−0.294317	+	0.0216528i
$266$	−8.33281			−0.510917
$267$			5.69208i			0.348349i
$268$			55.0011i			3.35973i
$269$	−15.5500			−0.948099			−0.474050	−	0.880498i	$-0.657208\pi$
$269$	−15.5500			−0.948099			−0.474050	+	0.880498i	$0.657208\pi$
$270$	0.406282	+	5.52241i	0.0247256	+	0.336083i
$271$	9.21039			0.559491			0.279746	−	0.960074i	$-0.409750\pi$
$271$	9.21039			0.559491			0.279746	+	0.960074i	$0.409750\pi$
$272$			16.6761i			1.01113i
$273$			10.8344i			0.655730i
$274$	29.4318			1.77804
$275$	−15.0370	+	2.22458i	−0.906767	+	0.134147i
$276$	29.3939			1.76930
$277$		−	15.0253i		−	0.902783i	−0.892326	−	0.451391i	$-0.850928\pi$
$277$		−	15.0253i		−	0.902783i	0.892326	−	0.451391i	$-0.149072\pi$
$278$			17.1860i			1.03075i
$279$	3.11926			0.186745
$280$	2.91525	+	39.6257i	0.174220	+	2.36809i
$281$	10.8200			0.645469			0.322734	−	0.946490i	$-0.395398\pi$
$281$	10.8200			0.645469			0.322734	+	0.946490i	$0.395398\pi$
$282$			15.6299i			0.930750i
$283$		−	2.29124i		−	0.136200i	−0.997678	−	0.0681001i	$-0.978306\pi$
$283$		−	2.29124i		−	0.136200i	0.997678	−	0.0681001i	$-0.0216937\pi$
$284$	−55.0011			−3.26372
$285$	2.23004	−	0.164064i	0.132096	−	0.00971828i
$286$	24.2404			1.43337
$287$			9.12572i			0.538674i
$288$		−	1.35510i		−	0.0798503i
$289$	4.99046			0.293556
$290$	49.5739	−	3.64714i	2.91108	−	0.214167i
$291$	8.82840			0.517530
$292$		−	6.69534i		−	0.391815i
$293$			19.5818i			1.14398i	0.820261	+	0.571989i	$0.193828\pi$
$293$			19.5818i			1.14398i	−0.820261	+	0.571989i	$0.806172\pi$
$294$	−10.7047			−0.624310
$295$	−1.81637	−	24.6891i	−0.105753	−	1.43745i
$296$	2.31769			0.134713
$297$			3.04014i			0.176407i
$298$			0.958598i			0.0555301i
$299$	−22.9025			−1.32449
$300$	−3.02384	−	20.4396i	−0.174582	−	1.18008i
$301$	25.2541			1.45562
$302$			39.1544i			2.25308i
$303$			17.7011i			1.01690i
$304$	−4.81205			−0.275990
$305$	1.16380	+	15.8190i	0.0666388	+	0.905791i
$306$	8.58181			0.490590
$307$		−	11.7388i		−	0.669967i	−0.942224	−	0.334984i	$-0.891269\pi$
$307$		−	11.7388i		−	0.669967i	0.942224	−	0.334984i	$-0.108731\pi$
$308$			42.2740i			2.40879i
$309$	−18.5287			−1.05406
$310$	−17.2259	+	1.26730i	−0.978363	+	0.0719779i
$311$	−26.6811			−1.51295			−0.756473	−	0.654025i	$-0.773079\pi$
$311$	−26.6811			−1.51295			−0.756473	+	0.654025i	$0.773079\pi$
$312$			17.0028i			0.962592i
$313$		−	5.95655i		−	0.336684i	−0.985729	−	0.168342i	$-0.946159\pi$
$313$		−	5.95655i		−	0.336684i	0.985729	−	0.168342i	$-0.0538413\pi$
$314$	−39.1190			−2.20761
$315$	7.50392	−	0.552062i	0.422798	−	0.0311052i
$316$	−33.4552			−1.88200
$317$		−	0.645531i		−	0.0362566i	−0.999836	−	0.0181283i	$-0.994229\pi$
$317$		−	0.645531i		−	0.0362566i	0.999836	−	0.0181283i	$-0.00577073\pi$
$318$		−	5.32037i		−	0.298351i
$319$	27.2909			1.52800
$320$	−1.02841	−	13.9787i	−0.0574899	−	0.781433i
$321$	10.7299			0.598882
$322$		−	59.2712i		−	3.30306i
$323$		−	3.46548i		−	0.192824i
$324$	−4.13242			−0.229579
$325$	2.35606	+	15.9257i	0.130691	+	0.883401i
$326$	15.8210			0.876243
$327$		−	4.26484i		−	0.235846i
$328$			14.3212i			0.790758i
$329$	21.2382			1.17090
$330$	−1.23516	−	16.7889i	−0.0679931	−	0.924199i
$331$	4.02020			0.220970			0.110485	−	0.993878i	$-0.464760\pi$
$331$	4.02020			0.220970			0.110485	+	0.993878i	$0.464760\pi$
$332$		−	63.8794i		−	3.50584i
$333$		−	0.438901i		−	0.0240517i
$334$	−50.6713			−2.77261
$335$	−29.6811	+	2.18363i	−1.62165	+	0.119304i
$336$	−16.1922			−0.883357
$337$		−	6.37467i		−	0.347250i	−0.984812	−	0.173625i	$-0.944452\pi$
$337$		−	6.37467i		−	0.347250i	0.984812	−	0.173625i	$-0.0555481\pi$
$338$			6.51977i			0.354629i
$339$	13.5016			0.733304
$340$	−31.9360	+	2.34952i	−1.73197	+	0.127421i
$341$	−9.48300			−0.513533
$342$			2.47637i			0.133907i
$343$		−	9.00881i		−	0.486430i
$344$	39.6320			2.13681
$345$	1.16698	+	15.8623i	0.0628283	+	0.853996i
$346$	27.7658			1.49270
$347$			13.5877i			0.729426i	0.931120	+	0.364713i	$0.118833\pi$
$347$			13.5877i			0.729426i	−0.931120	+	0.364713i	$0.881167\pi$
$348$			37.0961i			1.98856i
$349$	−35.4274			−1.89638			−0.948192	−	0.317696i	$-0.897091\pi$
$349$	−35.4274			−1.89638			−0.948192	+	0.317696i	$0.897091\pi$
$350$	−41.2155	+	6.09742i	−2.20306	+	0.325921i
$351$	3.21982			0.171861
$352$			4.11971i			0.219581i
$353$			12.1581i			0.647111i	0.946209	+	0.323556i	$0.104878\pi$
$353$			12.1581i			0.647111i	−0.946209	+	0.323556i	$0.895122\pi$
$354$	27.4163			1.45716
$355$	−2.18363	−	29.6811i	−0.115895	−	1.57531i
$356$	23.5221			1.24667
$357$		−	11.6611i		−	0.617170i
$358$			0.585602i			0.0309501i
$359$	21.5590			1.13784			0.568921	−	0.822392i	$-0.307361\pi$
$359$	21.5590			1.13784			0.568921	+	0.822392i	$0.307361\pi$
$360$	11.7761	−	0.866365i	0.620655	−	0.0456614i
$361$	1.00000			0.0526316
$362$		−	16.1699i		−	0.849872i
$363$			1.75755i			0.0922474i
$364$	44.7725			2.34671
$365$	3.61311	−	0.265815i	0.189119	−	0.0139134i
$366$	−17.5663			−0.918207
$367$			10.2026i			0.532571i	0.963894	+	0.266286i	$0.0857964\pi$
$367$			10.2026i			0.532571i	−0.963894	+	0.266286i	$0.914204\pi$
$368$		−	34.2281i		−	1.78426i
$369$	2.71201			0.141182
$370$	0.178318	+	2.42379i	0.00927031	+	0.126007i
$371$	−7.22938			−0.375331
$372$		−	12.8901i		−	0.668321i
$373$			17.2546i			0.893408i	0.894682	+	0.446704i	$0.147402\pi$
$373$			17.2546i			0.893408i	−0.894682	+	0.446704i	$0.852598\pi$
$374$	−26.0899			−1.34908
$375$	10.9101	−	2.44329i	0.563395	−	0.126171i
$376$	33.3296			1.71884
$377$		−	28.9038i		−	1.48862i
$378$			8.33281i			0.428594i
$379$	−2.62527			−0.134851			−0.0674254	−	0.997724i	$-0.521478\pi$
$379$	−2.62527			−0.134851			−0.0674254	+	0.997724i	$0.521478\pi$
$380$	−0.677979	−	9.21547i	−0.0347796	−	0.472743i
$381$	6.15097			0.315124
$382$			20.1290i			1.02989i
$383$			22.3767i			1.14340i	0.820464	+	0.571698i	$0.193715\pi$
$383$			22.3767i			1.14340i	−0.820464	+	0.571698i	$0.806285\pi$
$384$	18.2330			0.930449
$385$	−22.8130	+	1.67834i	−1.16266	+	0.0855364i
$386$	−4.49146			−0.228609
$387$		−	7.50511i		−	0.381506i
$388$		−	36.4827i		−	1.85213i
$389$	6.99517			0.354669			0.177335	−	0.984151i	$-0.443252\pi$
$389$	6.99517			0.354669			0.177335	+	0.984151i	$0.443252\pi$
$390$	−17.7811	+	1.30815i	−0.900383	+	0.0662410i
$391$	24.6499			1.24660
$392$			22.8269i			1.15293i
$393$		−	9.61327i		−	0.484925i
$394$	−17.8145			−0.897482
$395$	−1.32823	−	18.0540i	−0.0668303	−	0.908394i
$396$	12.5631			0.631321
$397$			26.9075i			1.35045i	0.737613	+	0.675223i	$0.235953\pi$
$397$			26.9075i			1.35045i	−0.737613	+	0.675223i	$0.764047\pi$
$398$			0.719462i			0.0360633i
$399$	3.36493			0.168457
$400$	−23.8012	+	3.52116i	−1.19006	+	0.176058i
$401$	−36.0076			−1.79813			−0.899066	−	0.437813i	$-0.855753\pi$
$401$	−36.0076			−1.79813			−0.899066	+	0.437813i	$0.855753\pi$
$402$		−	32.9597i		−	1.64388i
$403$			10.0435i			0.500300i
$404$	73.1483			3.63926
$405$	−0.164064	−	2.23004i	−0.00815238	−	0.110812i
$406$	74.8024			3.71238
$407$			1.33432i			0.0661399i
$408$		−	18.3000i		−	0.905986i
$409$	4.14087			0.204753			0.102376	−	0.994746i	$-0.467355\pi$
$409$	4.14087			0.204753			0.102376	+	0.994746i	$0.467355\pi$
$410$	−14.9769	+	1.10184i	−0.739654	+	0.0544161i
$411$	−11.8850			−0.586246
$412$			76.5686i			3.77226i
$413$		−	37.2536i		−	1.83313i
$414$	−17.6144			−0.865702
$415$	34.4722	−	2.53611i	1.69218	−	0.124493i
$416$	4.36319			0.213923
$417$		−	6.94000i		−	0.339853i
$418$		−	7.52852i		−	0.368232i
$419$	28.4394			1.38936			0.694678	−	0.719321i	$-0.255547\pi$
$419$	28.4394			1.38936			0.694678	+	0.719321i	$0.255547\pi$
$420$	−2.28135	−	31.0094i	−0.111319	−	1.51310i
$421$	−18.5057			−0.901912			−0.450956	−	0.892546i	$-0.648917\pi$
$421$	−18.5057			−0.901912			−0.450956	+	0.892546i	$0.648917\pi$
$422$		−	18.4882i		−	0.899994i
$423$		−	6.31163i		−	0.306882i
$424$	−11.3453			−0.550974
$425$	−2.53582	−	17.1408i	−0.123005	−	0.831453i
$426$	32.9597			1.59690
$427$			23.8693i			1.15512i
$428$		−	44.3403i		−	2.14327i
$429$	−9.78869			−0.472602
$430$	3.04919	+	41.4463i	0.147045	+	1.99872i
$431$	−6.11641			−0.294617			−0.147309	−	0.989091i	$-0.547061\pi$
$431$	−6.11641			−0.294617			−0.147309	+	0.989091i	$0.547061\pi$
$432$			4.81205i			0.231520i
$433$		−	14.1522i		−	0.680110i	−0.940406	−	0.340055i	$-0.889554\pi$
$433$		−	14.1522i		−	0.680110i	0.940406	−	0.340055i	$-0.110446\pi$
$434$	−25.9922			−1.24767
$435$	−20.0187	+	1.47277i	−0.959826	+	0.0706141i
$436$	−17.6241			−0.844042
$437$			7.11300i			0.340261i
$438$			4.01221i			0.191711i
$439$	−0.342806			−0.0163612			−0.00818061	−	0.999967i	$-0.502604\pi$
$439$	−0.342806			−0.0163612			−0.00818061	+	0.999967i	$0.502604\pi$
$440$	−35.8010	+	2.63387i	−1.70675	+	0.125565i
$441$	4.32273			0.205844
$442$			27.6319i			1.31431i
$443$			16.7686i			0.796699i	0.917234	+	0.398349i	$0.130417\pi$
$443$			16.7686i			0.796699i	−0.917234	+	0.398349i	$0.869583\pi$
$444$	−1.81373			−0.0860756
$445$	0.933862	+	12.6936i	0.0442693	+	0.601733i
$446$	68.9697			3.26581
$447$		−	0.387098i		−	0.0183091i
$448$		−	21.0926i		−	0.996531i
$449$	−8.85875			−0.418070			−0.209035	−	0.977908i	$-0.567032\pi$
$449$	−8.85875			−0.418070			−0.209035	+	0.977908i	$0.567032\pi$
$450$	1.81205	+	12.2485i	0.0854210	+	0.577402i
$451$	−8.24490			−0.388237
$452$		−	55.7941i		−	2.62434i
$453$		−	15.8112i		−	0.742875i
$454$	43.1893			2.02698
$455$	1.77754	+	24.1612i	0.0833322	+	1.13270i
$456$	5.28066			0.247290
$457$		−	30.2622i		−	1.41561i	−0.706409	−	0.707803i	$-0.749686\pi$
$457$		−	30.2622i		−	1.41561i	0.706409	−	0.707803i	$-0.250314\pi$
$458$		−	17.2639i		−	0.806690i
$459$	−3.46548			−0.161755
$460$	65.5496	−	4.82246i	3.05626	−	0.224849i
$461$	12.1116			0.564095			0.282048	−	0.959400i	$-0.408986\pi$
$461$	12.1116			0.564095			0.282048	+	0.959400i	$0.408986\pi$
$462$		−	25.3329i		−	1.17859i
$463$		−	15.0763i		−	0.700654i	−0.936628	−	0.350327i	$-0.886071\pi$
$463$		−	15.0763i		−	0.700654i	0.936628	−	0.350327i	$-0.113929\pi$
$464$	43.1971			2.00537
$465$	6.95608	−	0.511757i	0.322581	−	0.0237322i
$466$	21.6280			1.00190
$467$			11.1360i			0.515312i	0.966237	+	0.257656i	$0.0829502\pi$
$467$			11.1360i			0.515312i	−0.966237	+	0.257656i	$0.917050\pi$
$468$		−	13.3056i		−	0.615053i
$469$	−44.7860			−2.06803
$470$	2.56430	+	34.8554i	0.118283	+	1.60776i
$471$	15.7969			0.727882
$472$		−	58.4630i		−	2.69098i
$473$			22.8166i			1.04911i
$474$	20.0482			0.920845
$475$	4.94617	−	0.731737i	0.226946	−	0.0335744i
$476$	−48.1885			−2.20872
$477$			2.14845i			0.0983709i
$478$			29.6629i			1.35675i
$479$	−14.7878			−0.675673			−0.337837	−	0.941205i	$-0.609695\pi$
$479$	−14.7878			−0.675673			−0.337837	+	0.941205i	$0.609695\pi$
$480$	−0.222323	−	3.02194i	−0.0101476	−	0.137932i
$481$	1.41318			0.0644355
$482$			45.6549i			2.07952i
$483$			23.9347i			1.08907i
$484$	7.26293			0.330133
$485$	19.6877	−	1.44842i	0.893972	−	0.0657693i
$486$	2.47637			0.112331
$487$			39.9566i			1.81061i	0.424765	+	0.905303i	$0.360357\pi$
$487$			39.9566i			1.81061i	−0.424765	+	0.905303i	$0.639643\pi$
$488$			37.4588i			1.69568i
$489$	−6.38877			−0.288910
$490$	−23.8719	+	1.75625i	−1.07842	+	0.0793393i
$491$	−31.9841			−1.44342			−0.721712	−	0.692194i	$-0.756644\pi$
$491$	−31.9841			−1.44342			−0.721712	+	0.692194i	$0.756644\pi$
$492$		−	11.2072i		−	0.505258i
$493$			31.1091i			1.40108i
$494$	−7.97346			−0.358743
$495$	0.498776	+	6.77964i	0.0224183	+	0.304722i
$496$	−15.0101			−0.673972
$497$		−	44.7860i		−	2.00893i
$498$			38.2800i			1.71537i
$499$	−22.3704			−1.00143			−0.500717	−	0.865611i	$-0.666930\pi$
$499$	−22.3704			−1.00143			−0.500717	+	0.865611i	$0.666930\pi$
$500$	−10.0967	−	45.0851i	−0.451538	−	2.01627i
$501$	20.4619			0.914171
$502$			35.6390i			1.59065i
$503$		−	22.3837i		−	0.998039i	−0.866591	−	0.499019i	$-0.833694\pi$
$503$		−	22.3837i		−	0.998039i	0.866591	−	0.499019i	$-0.166306\pi$
$504$	17.7690			0.791496
$505$	2.90410	+	39.4741i	0.129231	+	1.75658i
$506$	53.5503			2.38060
$507$		−	2.63279i		−	0.116926i
$508$		−	25.4184i		−	1.12776i
$509$	−18.1912			−0.806313			−0.403156	−	0.915131i	$-0.632087\pi$
$509$	−18.1912			−0.806313			−0.403156	+	0.915131i	$0.632087\pi$
$510$	19.1378	−	1.40796i	0.847436	−	0.0623456i
$511$	5.45185			0.241175
$512$		−	44.3008i		−	1.95784i
$513$		−	1.00000i		−	0.0441511i
$514$	33.2142			1.46502
$515$	−41.3199	+	3.03989i	−1.82077	+	0.133954i
$516$	−31.0142			−1.36533
$517$			19.1882i			0.843898i
$518$			3.65728i			0.160692i
$519$	−11.2123			−0.492164
$520$	2.78953	+	37.9169i	0.122329	+	1.66276i
$521$	−12.3281			−0.540103			−0.270052	−	0.962846i	$-0.587041\pi$
$521$	−12.3281			−0.540103			−0.270052	+	0.962846i	$0.587041\pi$
$522$		−	22.2300i		−	0.972982i
$523$			9.23822i			0.403959i	0.979390	+	0.201980i	$0.0647375\pi$
$523$			9.23822i			0.403959i	−0.979390	+	0.201980i	$0.935263\pi$
$524$	−39.7261			−1.73544
$525$	16.6435	−	2.46224i	0.726381	−	0.107461i
$526$	9.53164			0.415599
$527$		−	10.8097i		−	0.470880i
$528$		−	14.6293i		−	0.636659i
$529$	−27.5947			−1.19977
$530$	−0.872878	−	11.8646i	−0.0379154	−	0.515367i
$531$	−11.0711			−0.480446
$532$		−	13.9053i		−	0.602871i
$533$			8.73218i			0.378233i
$534$	−14.0957			−0.609981
$535$	23.9280	−	1.76038i	1.03450	−	0.0761078i
$536$	−70.2839			−3.03580
$537$		−	0.236476i		−	0.0102047i
$538$		−	38.5075i		−	1.66018i
$539$	−13.1417			−0.566053
$540$	−9.21547	+	0.677979i	−0.396570	+	0.0291756i
$541$	−20.3908			−0.876668			−0.438334	−	0.898812i	$-0.644431\pi$
$541$	−20.3908			−0.876668			−0.438334	+	0.898812i	$0.644431\pi$
$542$			22.8083i			0.979702i
$543$			6.52968i			0.280215i
$544$	−4.69608			−0.201343
$545$	−0.699705	−	9.51077i	−0.0299721	−	0.407396i
$546$	−26.8301			−1.14822
$547$			29.4981i			1.26125i	0.776089	+	0.630623i	$0.217201\pi$
$547$			29.4981i			1.26125i	−0.776089	+	0.630623i	$0.782799\pi$
$548$			49.1140i			2.09804i
$549$	7.09357			0.302746
$550$	−5.50889	−	37.2373i	−0.234900	−	1.58780i
$551$	−8.97685			−0.382427
$552$			37.5613i			1.59872i
$553$		−	27.2418i		−	1.15844i
$554$	37.2082			1.58083
$555$	−0.0720077	−	0.978768i	−0.00305656	−	0.0415464i
$556$	−28.6790			−1.21626
$557$		−	41.3825i		−	1.75343i	−0.481009	−	0.876716i	$-0.659730\pi$
$557$		−	41.3825i		−	1.75343i	0.481009	−	0.876716i	$-0.340270\pi$
$558$			7.72446i			0.327002i
$559$	24.1651			1.02207
$560$	−36.1093	+	2.65655i	−1.52590	+	0.112260i
$561$	10.5355			0.444811
$562$			26.7944i			1.13025i
$563$		−	0.275090i		−	0.0115937i	−0.999983	−	0.00579684i	$-0.998155\pi$
$563$		−	0.275090i		−	0.0115937i	0.999983	−	0.00579684i	$-0.00184520\pi$
$564$	−26.0823			−1.09826
$565$	30.1090	−	2.21511i	1.26670	−	0.0931906i
$566$	5.67397			0.238495
$567$		−	3.36493i		−	0.141314i
$568$		−	70.2839i		−	2.94905i
$569$	16.9879			0.712170			0.356085	−	0.934453i	$-0.384111\pi$
$569$	16.9879			0.712170			0.356085	+	0.934453i	$0.384111\pi$
$570$	0.406282	+	5.52241i	0.0170173	+	0.231308i
$571$	−31.5915			−1.32206			−0.661031	−	0.750359i	$-0.729881\pi$
$571$	−31.5915			−1.32206			−0.661031	+	0.750359i	$0.729881\pi$
$572$			40.4510i			1.69134i
$573$		−	8.12841i		−	0.339569i
$574$	−22.5987			−0.943251
$575$	5.20484	+	35.1821i	0.217057	+	1.46719i
$576$	−6.26836			−0.261182
$577$			40.7290i			1.69557i	0.530340	+	0.847785i	$0.322064\pi$
$577$			40.7290i			1.69557i	−0.530340	+	0.847785i	$0.677936\pi$
$578$			12.3582i			0.514035i
$579$	1.81373			0.0753758
$580$	6.08612	+	82.7259i	0.252712	+	3.43500i
$581$	52.0154			2.15796
$582$			21.8624i			0.906226i
$583$		−	6.53159i		−	0.270511i
$584$	8.55572			0.354038
$585$	7.18032	−	0.528254i	0.296870	−	0.0218406i
$586$	−48.4917			−2.00317
$587$			8.89346i			0.367072i	0.983013	+	0.183536i	$0.0587544\pi$
$587$			8.89346i			0.367072i	−0.983013	+	0.183536i	$0.941246\pi$
$588$		−	17.8633i		−	0.736672i
$589$	3.11926			0.128527
$590$	61.1394	−	4.49801i	2.51707	−	0.185180i
$591$	7.19379			0.295913
$592$			2.11202i			0.0868034i
$593$		−	1.73890i		−	0.0714081i	−0.999362	−	0.0357041i	$-0.988633\pi$
$593$		−	1.73890i		−	0.0714081i	0.999362	−	0.0357041i	$-0.0113674\pi$
$594$	−7.52852			−0.308899
$595$	−1.91316	−	26.0047i	−0.0784318	−	1.06609i
$596$	−1.59965			−0.0655242
$597$		−	0.290530i		−	0.0118906i
$598$		−	56.7152i		−	2.31926i
$599$	−3.08221			−0.125936			−0.0629679	−	0.998016i	$-0.520057\pi$
$599$	−3.08221			−0.125936			−0.0629679	+	0.998016i	$0.520057\pi$
$600$	26.1190	−	3.86406i	1.06631	−	0.157749i
$601$	5.15472			0.210266			0.105133	−	0.994458i	$-0.466473\pi$
$601$	5.15472			0.210266			0.105133	+	0.994458i	$0.466473\pi$
$602$			62.5386i			2.54888i
$603$			13.3097i			0.542011i
$604$	−65.3385			−2.65859
$605$	0.288350	+	3.91941i	0.0117231	+	0.159347i
$606$	−43.8345			−1.78065
$607$			26.8041i			1.08794i	0.839104	+	0.543972i	$0.183080\pi$
$607$			26.8041i			1.08794i	−0.839104	+	0.543972i	$0.816920\pi$
$608$		−	1.35510i		−	0.0549567i
$609$	−30.2064			−1.22403
$610$	−39.1736	+	2.88199i	−1.58609	+	0.116688i
$611$	20.3223			0.822152
$612$			14.3208i			0.578884i
$613$			27.3062i			1.10289i	0.834212	+	0.551443i	$0.185923\pi$
$613$			27.3062i			1.10289i	−0.834212	+	0.551443i	$0.814077\pi$
$614$	29.0696			1.17315
$615$	6.04790	−	0.444942i	0.243875	−	0.0179418i
$616$	−54.0204			−2.17654
$617$			21.6982i			0.873535i	0.899575	+	0.436767i	$0.143877\pi$
$617$			21.6982i			0.873535i	−0.899575	+	0.436767i	$0.856123\pi$
$618$		−	45.8841i		−	1.84573i
$619$	−31.1815			−1.25329			−0.626644	−	0.779305i	$-0.715572\pi$
$619$	−31.1815			−1.25329			−0.626644	+	0.779305i	$0.715572\pi$
$620$	−2.11480	−	28.7455i	−0.0849323	−	1.15445i
$621$	7.11300			0.285435
$622$		−	66.0723i		−	2.64926i
$623$			19.1534i			0.767366i
$624$	−15.4939			−0.620253
$625$	23.9291	−	7.23858i	0.957165	−	0.289543i
$626$	14.7506			0.589554
$627$			3.04014i			0.121411i
$628$		−	65.2793i		−	2.60493i
$629$	−1.52100			−0.0606464
$630$	1.36711	+	18.5825i	0.0544670	+	0.740345i
$631$	−37.2639			−1.48345			−0.741726	−	0.670703i	$-0.765993\pi$
$631$	−37.2639			−1.48345			−0.741726	+	0.670703i	$0.765993\pi$
$632$		−	42.7512i		−	1.70055i
$633$			7.46586i			0.296741i
$634$	1.59857			0.0634875
$635$	13.7169	−	1.00915i	0.544339	−	0.0400469i
$636$	8.87831			0.352048
$637$			13.9184i			0.551467i
$638$			67.5824i			2.67561i
$639$	−13.3097			−0.526522
$640$	40.6604	−	2.99137i	1.60724	−	0.118244i
$641$	34.9211			1.37930			0.689650	−	0.724143i	$-0.257764\pi$
$641$	34.9211			1.37930			0.689650	+	0.724143i	$0.257764\pi$
$642$			26.5711i			1.04868i
$643$		−	11.4368i		−	0.451022i	−0.974241	−	0.225511i	$-0.927595\pi$
$643$		−	11.4368i		−	0.451022i	0.974241	−	0.225511i	$-0.0724051\pi$
$644$	98.9083			3.89753
$645$	−1.23131	−	16.7367i	−0.0484830	−	0.659007i
$646$	8.58181			0.337647
$647$		−	7.16181i		−	0.281560i	−0.990041	−	0.140780i	$-0.955039\pi$
$647$		−	7.16181i		−	0.281560i	0.990041	−	0.140780i	$-0.0449610\pi$
$648$		−	5.28066i		−	0.207444i
$649$	33.6578			1.32118
$650$	−39.4381	+	5.83447i	−1.54689	+	0.228847i
$651$	10.4961			0.411374
$652$			26.4011i			1.03395i
$653$			18.9906i			0.743160i	0.928401	+	0.371580i	$0.121184\pi$
$653$			18.9906i			0.743160i	−0.928401	+	0.371580i	$0.878816\pi$
$654$	10.5613			0.412981
$655$	−1.57719	−	21.4380i	−0.0616258	−	0.837651i
$656$	−13.0503			−0.509531
$657$		−	1.62020i		−	0.0632099i
$658$			52.5936i			2.05031i
$659$	−1.68493			−0.0656354			−0.0328177	−	0.999461i	$-0.510448\pi$
$659$	−1.68493			−0.0656354			−0.0328177	+	0.999461i	$0.510448\pi$
$660$	28.0163	−	2.06115i	1.09053	−	0.0802302i
$661$	33.5226			1.30388			0.651939	−	0.758271i	$-0.273956\pi$
$661$	33.5226			1.30388			0.651939	+	0.758271i	$0.273956\pi$
$662$			9.95550i			0.386932i
$663$		−	11.1582i		−	0.433349i
$664$	81.6291			3.16782
$665$	7.50392	−	0.552062i	0.290990	−	0.0214080i
$666$	1.08688			0.0421159
$667$		−	63.8523i		−	2.47237i
$668$		−	84.5572i		−	3.27162i
$669$	−27.8511			−1.07679
$670$	−5.40748	−	73.5014i	−0.208909	−	2.83961i
$671$	−21.5655			−0.832525
$672$		−	4.55983i		−	0.175899i
$673$		−	39.6506i		−	1.52842i	−0.644969	−	0.764209i	$-0.723130\pi$
$673$		−	39.6506i		−	1.52842i	0.644969	−	0.764209i	$-0.276870\pi$
$674$	15.7861			0.608056
$675$	−0.731737	−	4.94617i	−0.0281646	−	0.190378i
$676$	−10.8798			−0.418454
$677$		−	6.95042i		−	0.267126i	−0.991040	−	0.133563i	$-0.957358\pi$
$677$		−	6.95042i		−	0.267126i	0.991040	−	0.133563i	$-0.0426419\pi$
$678$			33.4349i			1.28406i
$679$	29.7069			1.14005
$680$	−3.00237	−	40.8098i	−0.115136	−	1.56499i
$681$	−17.4406			−0.668324
$682$		−	23.4834i		−	0.899227i
$683$		−	18.9576i		−	0.725392i	−0.931908	−	0.362696i	$-0.881856\pi$
$683$		−	18.9576i		−	0.725392i	0.931908	−	0.362696i	$-0.118144\pi$
$684$	−4.13242			−0.158007
$685$	−26.5041	+	1.94990i	−1.01267	+	0.0745019i
$686$	22.3092			0.851768
$687$			6.97146i			0.265978i
$688$			36.1150i			1.37687i
$689$	−6.91762			−0.263540
$690$	−39.2809	+	2.88988i	−1.49540	+	0.110016i
$691$	−31.6038			−1.20226			−0.601132	−	0.799150i	$-0.705283\pi$
$691$	−31.6038			−1.20226			−0.601132	+	0.799150i	$0.705283\pi$
$692$			46.3338i			1.76135i
$693$			10.2298i			0.388600i
$694$	−33.6482			−1.27727
$695$	−1.13860	−	15.4765i	−0.0431896	−	0.587057i
$696$	−47.4037			−1.79683
$697$		−	9.39842i		−	0.355991i
$698$		−	87.7314i		−	3.32068i
$699$	−8.73376			−0.330341
$700$	−10.1750	−	68.7779i	−0.384579	−	2.59956i
$701$	−17.4683			−0.659770			−0.329885	−	0.944021i	$-0.607010\pi$
$701$	−17.4683			−0.659770			−0.329885	+	0.944021i	$0.607010\pi$
$702$			7.97346i			0.300939i
$703$		−	0.438901i		−	0.0165535i
$704$	19.0567			0.718226
$705$	−1.03551	−	14.0752i	−0.0389995	−	0.530102i
$706$	−30.1080			−1.13313
$707$			59.5628i			2.24009i
$708$			45.7506i			1.71941i
$709$	−16.4473			−0.617691			−0.308846	−	0.951112i	$-0.599943\pi$
$709$	−16.4473			−0.617691			−0.308846	+	0.951112i	$0.599943\pi$
$710$	73.5014	−	5.40748i	2.75846	−	0.202939i
$711$	−8.09580			−0.303616
$712$			30.0580i			1.12647i
$713$			22.1873i			0.830921i
$714$	28.8772			1.08070
$715$	−21.8292	+	1.60597i	−0.816365	+	0.0600598i
$716$	−0.977218			−0.0365203
$717$		−	11.9784i		−	0.447340i
$718$			53.3882i			1.99243i
$719$	−25.6670			−0.957219			−0.478610	−	0.878028i	$-0.658859\pi$
$719$	−25.6670			−0.957219			−0.478610	+	0.878028i	$0.658859\pi$
$720$	0.789482	+	10.7311i	0.0294223	+	0.399924i
$721$	−62.3479			−2.32196
$722$			2.47637i			0.0921610i
$723$		−	18.4362i		−	0.685649i
$724$	26.9834			1.00283
$725$	−44.4010	+	6.56869i	−1.64901	+	0.243955i
$726$	−4.35235			−0.161531
$727$			2.84193i			0.105401i	0.998610	+	0.0527007i	$0.0167829\pi$
$727$			2.84193i			0.105401i	−0.998610	+	0.0527007i	$0.983217\pi$
$728$			57.2131i			2.12046i
$729$	−1.00000			−0.0370370
$730$	0.658258	+	8.94740i	0.0243632	+	0.331158i
$731$	−26.0088			−0.961970
$732$		−	29.3136i		−	1.08346i
$733$			9.44601i			0.348896i	0.984666	+	0.174448i	$0.0558141\pi$
$733$			9.44601i			0.348896i	−0.984666	+	0.174448i	$0.944186\pi$
$734$	−25.2654			−0.932564
$735$	9.63987	−	0.709202i	0.355572	−	0.0261593i
$736$	9.63885			0.355293
$737$		−	40.4632i		−	1.49048i
$738$			6.71595i			0.247218i
$739$	−47.7890			−1.75795			−0.878973	−	0.476872i	$-0.841770\pi$
$739$	−47.7890			−1.75795			−0.878973	+	0.476872i	$0.841770\pi$
$740$	−4.04468	+	0.297566i	−0.148685	+	0.0109387i
$741$	3.21982			0.118283
$742$		−	17.9026i		−	0.657227i
$743$		−	17.5073i		−	0.642280i	−0.947032	−	0.321140i	$-0.895934\pi$
$743$		−	17.5073i		−	0.642280i	0.947032	−	0.321140i	$-0.104066\pi$
$744$	16.4718			0.603885
$745$	−0.0635086	−	0.863244i	−0.00232678	−	0.0316268i
$746$	−42.7287			−1.56441
$747$		−	15.4581i		−	0.565583i
$748$		−	43.5373i		−	1.59188i
$749$	36.1052			1.31925
$750$	6.05049	+	27.0175i	0.220933	+	0.986539i
$751$	52.0788			1.90038			0.950191	−	0.311667i	$-0.100887\pi$
$751$	52.0788			1.90038			0.950191	+	0.311667i	$0.100887\pi$
$752$			30.3719i			1.10755i
$753$		−	14.3916i		−	0.524460i
$754$	71.5766			2.60667
$755$	−2.59404	−	35.2596i	−0.0944068	−	1.28323i
$756$	−13.9053			−0.505730
$757$		−	21.4153i		−	0.778351i	−0.921164	−	0.389175i	$-0.872760\pi$
$757$		−	21.4153i		−	0.778351i	0.921164	−	0.389175i	$-0.127240\pi$
$758$		−	6.50113i		−	0.236132i
$759$	−21.6245			−0.784920
$760$	11.7761	−	0.866365i	0.427164	−	0.0314263i
$761$	−28.5216			−1.03391			−0.516953	−	0.856014i	$-0.672934\pi$
$761$	−28.5216			−1.03391			−0.516953	+	0.856014i	$0.672934\pi$
$762$			15.2321i			0.551801i
$763$		−	14.3509i		−	0.519536i
$764$	−33.5900			−1.21524
$765$	−7.72816	+	0.568559i	−0.279412	+	0.0205563i
$766$	−55.4130			−2.00215
$767$		−	35.6470i		−	1.28714i
$768$			32.6150i			1.17689i
$769$	29.4340			1.06142			0.530709	−	0.847554i	$-0.321926\pi$
$769$	29.4340			1.06142			0.530709	+	0.847554i	$0.321926\pi$
$770$	−4.15621	−	56.4934i	−0.149779	−	2.03588i
$771$	−13.4124			−0.483037
$772$		−	7.49507i		−	0.269754i
$773$			25.2029i			0.906484i	0.891387	+	0.453242i	$0.149733\pi$
$773$			25.2029i			0.906484i	−0.891387	+	0.453242i	$0.850267\pi$
$774$	18.5854			0.668040
$775$	15.4284	−	2.28248i	0.554204	−	0.0819891i
$776$	46.6198			1.67355
$777$		−	1.47687i		−	0.0529825i
$778$			17.3227i			0.621047i
$779$	2.71201			0.0971679
$780$	−2.18297	−	29.6721i	−0.0781628	−	1.06243i
$781$	40.4632			1.44789
$782$			61.0424i			2.18287i
$783$			8.97685i			0.320807i
$784$	−20.8012			−0.742900
$785$	35.2277	−	2.59169i	1.25733	−	0.0925014i
$786$	23.8060			0.849133
$787$			7.63245i			0.272067i	0.990704	+	0.136034i	$0.0434355\pi$
$787$			7.63245i			0.272067i	−0.990704	+	0.136034i	$0.956564\pi$
$788$		−	29.7278i		−	1.05901i
$789$	−3.84903			−0.137029
$790$	44.7083	−	3.28918i	1.59065	−	0.117024i
$791$	45.4318			1.61537
$792$			16.0540i			0.570453i
$793$			22.8400i			0.811072i
$794$	−66.6329			−2.36471
$795$	0.352483	+	4.79114i	0.0125013	+	0.169924i
$796$	−1.20059			−0.0425539
$797$			16.0606i			0.568896i	0.958691	+	0.284448i	$0.0918104\pi$
$797$			16.0606i			0.568896i	−0.958691	+	0.284448i	$0.908190\pi$
$798$			8.33281i			0.294978i
$799$	−21.8728			−0.773805
$800$	−0.991580	−	6.70257i	−0.0350576	−	0.236972i
$801$	5.69208			0.201120
$802$		−	89.1682i		−	3.14864i
$803$			4.92563i			0.173822i
$804$	55.0011			1.93974
$805$	3.92681	+	53.3754i	0.138402	+	1.88124i
$806$	−24.8713			−0.876055
$807$			15.5500i			0.547385i
$808$			93.4735i			3.28838i
$809$	−4.93203			−0.173401			−0.0867004	−	0.996234i	$-0.527632\pi$
$809$	−4.93203			−0.173401			−0.0867004	+	0.996234i	$0.527632\pi$
$810$	5.52241	−	0.406282i	0.194038	−	0.0142753i
$811$	25.7027			0.902543			0.451272	−	0.892387i	$-0.350971\pi$
$811$	25.7027			0.902543			0.451272	+	0.892387i	$0.350971\pi$
$812$			124.826i			4.38052i
$813$		−	9.21039i		−	0.323022i
$814$	−3.30428			−0.115815
$815$	−14.2472	+	1.04816i	−0.499058	+	0.0367156i
$816$	16.6761			0.583779
$817$		−	7.50511i		−	0.262570i
$818$			10.2543i			0.358534i
$819$	10.8344			0.378586
$820$	−1.83869	−	24.9925i	−0.0642098	−	0.872775i
$821$	27.2252			0.950167			0.475083	−	0.879941i	$-0.342418\pi$
$821$	27.2252			0.950167			0.475083	+	0.879941i	$0.342418\pi$
$822$		−	29.4318i		−	1.02655i
$823$			2.80990i			0.0979470i	0.998800	+	0.0489735i	$0.0155950\pi$
$823$			2.80990i			0.0979470i	−0.998800	+	0.0489735i	$0.984405\pi$
$824$	−97.8441			−3.40856
$825$	2.22458	+	15.0370i	0.0774500	+	0.523522i
$826$	92.2537			3.20992
$827$		−	7.26341i		−	0.252573i	−0.991994	−	0.126287i	$-0.959694\pi$
$827$		−	7.26341i		−	0.252573i	0.991994	−	0.126287i	$-0.0403059\pi$
$828$		−	29.3939i		−	1.02151i
$829$	−10.0416			−0.348758			−0.174379	−	0.984679i	$-0.555792\pi$
$829$	−10.0416			−0.348758			−0.174379	+	0.984679i	$0.555792\pi$
$830$	6.28036	+	85.3661i	0.217994	+	2.96310i
$831$	−15.0253			−0.521222
$832$		−	20.1830i		−	0.699719i
$833$		−	14.9803i		−	0.519038i
$834$	17.1860			0.595103
$835$	45.6309	−	3.35705i	1.57912	−	0.116176i
$836$	12.5631			0.434505
$837$		−	3.11926i		−	0.107818i
$838$			70.4266i			2.43284i
$839$	33.4255			1.15397			0.576987	−	0.816753i	$-0.304228\pi$
$839$	33.4255			1.15397			0.576987	+	0.816753i	$0.304228\pi$
$840$	39.6257	−	2.91525i	1.36722	−	0.100586i
$841$	51.5839			1.77875
$842$		−	45.8270i		−	1.57930i
$843$		−	10.8200i		−	0.372661i
$844$	30.8521			1.06197
$845$	−0.431945	−	5.87123i	−0.0148594	−	0.201977i
$846$	15.6299			0.537369
$847$			5.91402i			0.203208i
$848$		−	10.3385i		−	0.355024i
$849$	−2.29124			−0.0786353
$850$	42.4471	−	6.27963i	1.45592	−	0.215390i
$851$	3.12190			0.107017
$852$			55.0011i			1.88431i
$853$			45.0071i			1.54101i	0.637432	+	0.770507i	$0.279997\pi$
$853$			45.0071i			1.54101i	−0.637432	+	0.770507i	$0.720003\pi$
$854$	−59.1094			−2.02268
$855$	−0.164064	−	2.23004i	−0.00561085	−	0.0762658i
$856$	56.6608			1.93662
$857$			0.677201i			0.0231328i	0.999933	+	0.0115664i	$0.00368177\pi$
$857$			0.677201i			0.0231328i	−0.999933	+	0.0115664i	$0.996318\pi$
$858$		−	24.2404i		−	0.827555i
$859$	−41.7947			−1.42602			−0.713008	−	0.701156i	$-0.752668\pi$
$859$	−41.7947			−1.42602			−0.713008	+	0.701156i	$0.752668\pi$
$860$	−69.1630	+	5.08831i	−2.35844	+	0.173510i
$861$	9.12572			0.311004
$862$		−	15.1465i		−	0.515892i
$863$		−	5.56037i		−	0.189277i	−0.995512	−	0.0946386i	$-0.969830\pi$
$863$		−	5.56037i		−	0.189277i	0.995512	−	0.0946386i	$-0.0301696\pi$
$864$	−1.35510			−0.0461016
$865$	−25.0038	+	1.83952i	−0.850156	+	0.0625457i
$866$	35.0460			1.19091
$867$		−	4.99046i		−	0.169485i
$868$		−	43.3743i		−	1.47222i
$869$	24.6124			0.834917
$870$	−3.64714	−	49.5739i	−0.123650	−	1.68071i
$871$	−42.8547			−1.45207
$872$		−	22.5212i		−	0.762664i
$873$		−	8.82840i		−	0.298796i
$874$	−17.6144			−0.595817
$875$	36.7117	−	8.22149i	1.24108	−	0.277937i
$876$	−6.69534			−0.226214
$877$			11.4181i			0.385561i	0.981242	+	0.192780i	$0.0617505\pi$
$877$			11.4181i			0.385561i	−0.981242	+	0.192780i	$0.938249\pi$
$878$		−	0.848915i		−	0.0286495i
$879$	19.5818			0.660476
$880$	−2.40014	−	32.6240i	−0.0809086	−	1.09975i
$881$	−15.9832			−0.538487			−0.269244	−	0.963072i	$-0.586774\pi$
$881$	−15.9832			−0.538487			−0.269244	+	0.963072i	$0.586774\pi$
$882$			10.7047i			0.360446i
$883$		−	24.9699i		−	0.840303i	−0.907454	−	0.420152i	$-0.861977\pi$
$883$		−	24.9699i		−	0.840303i	0.907454	−	0.420152i	$-0.138023\pi$
$884$	−46.1104			−1.55086
$885$	−24.6891	+	1.81637i	−0.829915	+	0.0610566i
$886$	−41.5252			−1.39507
$887$		−	52.4889i		−	1.76241i	−0.472739	−	0.881203i	$-0.656735\pi$
$887$		−	52.4889i		−	1.76241i	0.472739	−	0.881203i	$-0.343265\pi$
$888$		−	2.31769i		−	0.0777766i
$889$	20.6976			0.694174
$890$	−31.4340	+	2.31259i	−1.05367	+	0.0775182i
$891$	3.04014			0.101849
$892$			115.093i			3.85358i
$893$		−	6.31163i		−	0.211211i
$894$	0.958598			0.0320603
$895$	−0.0387971	−	0.527351i	−0.00129684	−	0.0176274i
$896$	61.3527			2.04965
$897$			22.9025i			0.764693i
$898$		−	21.9376i		−	0.732066i
$899$	−28.0012			−0.933891
$900$	−20.4396	+	3.02384i	−0.681321	+	0.100795i
$901$	7.44541			0.248043
$902$		−	20.4174i		−	0.679826i
$903$		−	25.2541i		−	0.840405i
$904$	71.2972			2.37131
$905$	1.07128	+	14.5615i	0.0356106	+	0.484039i
$906$	39.1544			1.30082
$907$		−	20.0034i		−	0.664201i	−0.943244	−	0.332101i	$-0.892243\pi$
$907$		−	20.0034i		−	0.664201i	0.943244	−	0.332101i	$-0.107757\pi$
$908$			72.0717i			2.39178i
$909$	17.7011			0.587108
$910$	−59.8322	+	4.40184i	−1.98342	+	0.145920i
$911$	28.5727			0.946655			0.473328	−	0.880886i	$-0.343053\pi$
$911$	28.5727			0.946655			0.473328	+	0.880886i	$0.343053\pi$
$912$			4.81205i			0.159343i
$913$			46.9948i			1.55530i
$914$	74.9405			2.47881
$915$	15.8190	−	1.16380i	0.522959	−	0.0384739i
$916$	28.8090			0.951876
$917$		−	32.3479i		−	1.06822i
$918$		−	8.58181i		−	0.283242i
$919$	0.610155			0.0201272			0.0100636	−	0.999949i	$-0.496797\pi$
$919$	0.610155			0.0201272			0.0100636	+	0.999949i	$0.496797\pi$
$920$	6.16245	+	83.7633i	0.203170	+	2.76160i
$921$	−11.7388			−0.386806
$922$			29.9929i			0.987765i
$923$		−	42.8547i		−	1.41058i
$924$	42.2740			1.39071
$925$	−0.321160	−	2.17088i	−0.0105597	−	0.0713781i
$926$	37.3345			1.22689
$927$			18.5287i			0.608564i
$928$			12.1646i			0.399322i
$929$	2.65447			0.0870905			0.0435452	−	0.999051i	$-0.486135\pi$
$929$	2.65447			0.0870905			0.0435452	+	0.999051i	$0.486135\pi$
$930$	1.26730	+	17.2259i	0.0415565	+	0.564858i
$931$	4.32273			0.141672
$932$			36.0916i			1.18222i
$933$			26.6811i			0.873500i
$934$	−27.5769			−0.902343
$935$	23.4947	−	1.72850i	0.768358	−	0.0565279i
$936$	17.0028			0.555753
$937$			31.8629i			1.04092i	0.853887	+	0.520458i	$0.174239\pi$
$937$			31.8629i			1.04092i	−0.853887	+	0.520458i	$0.825761\pi$
$938$		−	110.907i		−	3.62124i
$939$	−5.95655			−0.194385
$940$	−58.1646	+	4.27915i	−1.89712	+	0.139571i
$941$	44.8069			1.46066			0.730332	−	0.683092i	$-0.239365\pi$
$941$	44.8069			1.46066			0.730332	+	0.683092i	$0.239365\pi$
$942$			39.1190i			1.27456i
$943$			19.2905i			0.628186i
$944$	53.2749			1.73395
$945$	−0.552062	−	7.50392i	−0.0179586	−	0.244103i
$946$	−56.5023			−1.83705
$947$			12.4058i			0.403135i	0.979475	+	0.201568i	$0.0646035\pi$
$947$			12.4058i			0.403135i	−0.979475	+	0.201568i	$0.935396\pi$
$948$			33.4552i			1.08658i
$949$	5.21674			0.169342
$950$	1.81205	+	12.2485i	0.0587908	+	0.397395i
$951$	−0.645531			−0.0209328
$952$		−	61.5783i		−	1.99576i
$953$			29.9975i			0.971715i	0.874038	+	0.485858i	$0.161493\pi$
$953$			29.9975i			0.971715i	−0.874038	+	0.485858i	$0.838507\pi$
$954$	−5.32037			−0.172253
$955$	−1.33358	−	18.1267i	−0.0431535	−	0.586566i
$956$	−49.4997			−1.60093
$957$		−	27.2909i		−	0.882189i
$958$		−	36.6202i		−	1.18314i
$959$	−39.9923			−1.29142
$960$	−13.9787	+	1.02841i	−0.451161	+	0.0331918i
$961$	−21.2702			−0.686135
$962$			3.49956i			0.112830i
$963$		−	10.7299i		−	0.345765i
$964$	−76.1861			−2.45379
$965$	4.04468	−	0.297566i	0.130203	−	0.00957899i
$966$	−59.2712			−1.90702
$967$		−	6.68769i		−	0.215062i	−0.994202	−	0.107531i	$-0.965706\pi$
$967$		−	6.68769i		−	0.215062i	0.994202	−	0.107531i	$-0.0342944\pi$
$968$			9.28103i			0.298304i
$969$	−3.46548			−0.111327
$970$	3.58682	+	48.7541i	0.115166	+	1.56540i
$971$	6.14156			0.197092			0.0985460	−	0.995132i	$-0.468581\pi$
$971$	6.14156			0.197092			0.0985460	+	0.995132i	$0.468581\pi$
$972$			4.13242i			0.132547i
$973$		−	23.3526i		−	0.748650i
$974$	−98.9474			−3.17048
$975$	15.9257	−	2.35606i	0.510032	−	0.0754542i
$976$	−34.1346			−1.09262
$977$			30.0427i			0.961153i	0.876953	+	0.480576i	$0.159572\pi$
$977$			30.0427i			0.961153i	−0.876953	+	0.480576i	$0.840428\pi$
$978$		−	15.8210i		−	0.505899i
$979$	−17.3047			−0.553061
$980$	−2.93072	−	39.8360i	−0.0936185	−	1.27251i
$981$	−4.26484			−0.136166
$982$		−	79.2046i		−	2.52752i
$983$			46.2506i			1.47516i	0.675258	+	0.737582i	$0.264032\pi$
$983$			46.2506i			1.47516i	−0.675258	+	0.737582i	$0.735968\pi$
$984$	14.3212			0.456544
$985$	16.0425	−	1.18024i	0.511155	−	0.0376055i
$986$	−77.0377			−2.45338
$987$		−	21.2382i		−	0.676018i
$988$		−	13.3056i		−	0.423308i
$989$	53.3838			1.69751
$990$	−16.7889	+	1.23516i	−0.533586	+	0.0392558i
$991$	−30.4226			−0.966407			−0.483203	−	0.875508i	$-0.660527\pi$
$991$	−30.4226			−0.966407			−0.483203	+	0.875508i	$0.660527\pi$
$992$		−	4.22693i		−	0.134205i
$993$		−	4.02020i		−	0.127577i
$994$	110.907			3.51775
$995$	−0.0476655	−	0.647895i	−0.00151110	−	0.0205396i
$996$	−63.8794			−2.02410
$997$			15.9718i			0.505833i	0.967488	+	0.252916i	$0.0813898\pi$
$997$			15.9718i			0.505833i	−0.967488	+	0.252916i	$0.918610\pi$
$998$		−	55.3973i		−	1.75357i
$999$	−0.438901			−0.0138862

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.2.c.b.229.13	yes	14
3.2	odd	2		855.2.c.g.514.2		14
5.2	odd	4		1425.2.a.y.1.2		7
5.3	odd	4		1425.2.a.z.1.6		7
5.4	even	2	inner	285.2.c.b.229.2	✓	14
15.2	even	4		4275.2.a.bw.1.6		7
15.8	even	4		4275.2.a.bv.1.2		7
15.14	odd	2		855.2.c.g.514.13		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.c.b.229.2	✓	14	5.4	even	2	inner
285.2.c.b.229.13	yes	14	1.1	even	1	trivial
855.2.c.g.514.2		14	3.2	odd	2
855.2.c.g.514.13		14	15.14	odd	2
1425.2.a.y.1.2		7	5.2	odd	4
1425.2.a.z.1.6		7	5.3	odd	4
4275.2.a.bv.1.2		7	15.8	even	4
4275.2.a.bw.1.6		7	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	285.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.47637i q^{2} -1.00000i q^{3} -4.13242 q^{4} +(-0.164064 - 2.23004i) q^{5} +2.47637 q^{6} -3.36493i q^{7} -5.28066i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+2.47637i q^{2} -1.00000i q^{3} -4.13242 q^{4} +(-0.164064 - 2.23004i) q^{5} +2.47637 q^{6} -3.36493i q^{7} -5.28066i q^{8} -1.00000 q^{9} +(5.52241 - 0.406282i) q^{10} +3.04014 q^{11} +4.13242i q^{12} -3.21982i q^{13} +8.33281 q^{14} +(-2.23004 + 0.164064i) q^{15} +4.81205 q^{16} +3.46548i q^{17} -2.47637i q^{18} -1.00000 q^{19} +(0.677979 + 9.21547i) q^{20} -3.36493 q^{21} +7.52852i q^{22} -7.11300i q^{23} -5.28066 q^{24} +(-4.94617 + 0.731737i) q^{25} +7.97346 q^{26} +1.00000i q^{27} +13.9053i q^{28} +8.97685 q^{29} +(-0.406282 - 5.52241i) q^{30} -3.11926 q^{31} +1.35510i q^{32} -3.04014i q^{33} -8.58181 q^{34} +(-7.50392 + 0.552062i) q^{35} +4.13242 q^{36} +0.438901i q^{37} -2.47637i q^{38} -3.21982 q^{39} +(-11.7761 + 0.866365i) q^{40} -2.71201 q^{41} -8.33281i q^{42} +7.50511i q^{43} -12.5631 q^{44} +(0.164064 + 2.23004i) q^{45} +17.6144 q^{46} +6.31163i q^{47} -4.81205i q^{48} -4.32273 q^{49} +(-1.81205 - 12.2485i) q^{50} +3.46548 q^{51} +13.3056i q^{52} -2.14845i q^{53} -2.47637 q^{54} +(-0.498776 - 6.77964i) q^{55} -17.7690 q^{56} +1.00000i q^{57} +22.2300i q^{58} +11.0711 q^{59} +(9.21547 - 0.677979i) q^{60} -7.09357 q^{61} -7.72446i q^{62} +3.36493i q^{63} +6.26836 q^{64} +(-7.18032 + 0.528254i) q^{65} +7.52852 q^{66} -13.3097i q^{67} -14.3208i q^{68} -7.11300 q^{69} +(-1.36711 - 18.5825i) q^{70} +13.3097 q^{71} +5.28066i q^{72} +1.62020i q^{73} -1.08688 q^{74} +(0.731737 + 4.94617i) q^{75} +4.13242 q^{76} -10.2298i q^{77} -7.97346i q^{78} +8.09580 q^{79} +(-0.789482 - 10.7311i) q^{80} +1.00000 q^{81} -6.71595i q^{82} +15.4581i q^{83} +13.9053 q^{84} +(7.72816 - 0.568559i) q^{85} -18.5854 q^{86} -8.97685i q^{87} -16.0540i q^{88} -5.69208 q^{89} +(-5.52241 + 0.406282i) q^{90} -10.8344 q^{91} +29.3939i q^{92} +3.11926i q^{93} -15.6299 q^{94} +(0.164064 + 2.23004i) q^{95} +1.35510 q^{96} +8.82840i q^{97} -10.7047i q^{98} -3.04014 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 22 q^{4} + 2 q^{5} + 6 q^{6} - 14 q^{9}+O(q^{10}) \) 14 * q - 22 * q^4 + 2 * q^5 + 6 * q^6 - 14 * q^9	\( 14 q - 22 q^{4} + 2 q^{5} + 6 q^{6} - 14 q^{9} + 2 q^{10} - 8 q^{11} + 8 q^{14} - 2 q^{15} + 38 q^{16} - 14 q^{19} + 12 q^{20} + 16 q^{21} - 18 q^{24} - 4 q^{25} - 40 q^{26} + 12 q^{29} + 4 q^{30} + 8 q^{31} - 4 q^{34} - 14 q^{35} + 22 q^{36} - 16 q^{39} + 18 q^{40} + 4 q^{41} + 64 q^{44} - 2 q^{45} - 8 q^{46} - 34 q^{49} + 4 q^{50} + 8 q^{51} - 6 q^{54} - 2 q^{55} - 44 q^{56} + 36 q^{59} - 18 q^{60} + 24 q^{61} - 22 q^{64} - 12 q^{65} + 24 q^{66} - 20 q^{69} - 60 q^{70} - 36 q^{71} - 12 q^{74} + 22 q^{76} + 8 q^{79} + 36 q^{80} + 14 q^{81} - 28 q^{84} - 18 q^{85} - 92 q^{86} + 16 q^{89} - 2 q^{90} + 24 q^{91} + 40 q^{94} - 2 q^{95} + 62 q^{96} + 8 q^{99}+O(q^{100}) \) 14 * q - 22 * q^4 + 2 * q^5 + 6 * q^6 - 14 * q^9 + 2 * q^10 - 8 * q^11 + 8 * q^14 - 2 * q^15 + 38 * q^16 - 14 * q^19 + 12 * q^20 + 16 * q^21 - 18 * q^24 - 4 * q^25 - 40 * q^26 + 12 * q^29 + 4 * q^30 + 8 * q^31 - 4 * q^34 - 14 * q^35 + 22 * q^36 - 16 * q^39 + 18 * q^40 + 4 * q^41 + 64 * q^44 - 2 * q^45 - 8 * q^46 - 34 * q^49 + 4 * q^50 + 8 * q^51 - 6 * q^54 - 2 * q^55 - 44 * q^56 + 36 * q^59 - 18 * q^60 + 24 * q^61 - 22 * q^64 - 12 * q^65 + 24 * q^66 - 20 * q^69 - 60 * q^70 - 36 * q^71 - 12 * q^74 + 22 * q^76 + 8 * q^79 + 36 * q^80 + 14 * q^81 - 28 * q^84 - 18 * q^85 - 92 * q^86 + 16 * q^89 - 2 * q^90 + 24 * q^91 + 40 * q^94 - 2 * q^95 + 62 * q^96 + 8 * q^99

Introduction

L-functions

Modular forms

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